As for Mengele, it is believed that they did not even try to bring him to justice. After the war, he lived openly in Germany for several years, and when it smelled of kerosene, he rushed to Argentina. I must say that in Buenos Aires he did not hide much. He lived for himself and even provided medical services. He was arrested for doing abortions. MOSSAD, when planning to capture Eichmann, knew about the whereabouts of Mengele. We thought to take both, but decided that it would be too big a risk. As a result, only Eichmann was captured, and Mengele collected his things and blew into Paraguay. There, at that time, was ruled by Alfredo Stroessner, who gathered Nazis from all over South America. After that, Mengele's trail was lost. Many years later, it turned out that he drowned in a bay near the city of Sao Paulo, Brazil. Except for MOSSAD, no one hunted him. And so it was with a lot of doctors who tortured prisoners of the camps. Moreover, we do not even know the names of many sadistic doctors.
To some extent, yes, but not all of them. Basically, of course, the highest ranks and the most famous doctors who carried out experiments on prisoners went on trial. In particular, in the case against doctors in Nuremberg in 1947, 23 people appeared before the court, of whom 16 were found guilty, and seven were sentenced to be shot.
Some of the scientists indirectly related to the activities in concentration camps remained to work in post-war Germany, some even held very high posts in institutions. For example, Ottmar von Verschuer, scientific director of the famous Dr. Mengele, in 1951 headed the Institute of Genetics. Others, like Joseph Mengele, known for his experiments on children and other prisoners (you can read more about them here), fled the country, like other prominent Nazis, to the countries of South America. Mengele died there, justice never caught up with him.